Sanding down glaze drips on Cone 6 ware

I experimented with using wire stilts on cone 6 ware recently, and it worked well enough -- that is, the wire did not melt, and the pieces mostly remained standing! -- but I did have a few pooling glaze drips on the bottoms of pieces where they were sitting on the stilts. This was mostly because of the kind of glazes I chose to use (lesson learned). I'd like to grind these bumps down smooth, so that the pieces are stable. What is the best sanding attachment for my drill for this job? I've seen all kinds of sanding discs at the hardware store -- some for removing paint from metal -- some rough synthetic looking discs, and regular sandpaper of various grit levels.
Any suggestion for what to use to smooth down glaze? My dremel grinding stones aren't quite doing the job.

Holder.jpg12.36KB58 downloads I use a diamond disc in my dremel tool. Also try to drip some water on it as I grind. Being a sort of new potter I'm always looking for suggestions from more experienced potters, and I picked up this trick. I try to cut a shallow depression near the bottom of each piece to give excess glaze a little place to pool up in. Also wiping with a sponge around the edge of the bottom has helped. Here is a picture of a utensil holder with real runny glaze that this process worked on.

I have safety glasses. I think someone on here suggested storing them in an old odd sock to prevent them from scratching in a toolbox.Marcia

I have gotten used to using sanding discs on the wheel head-Harbor Freight has some discs that are white, that work extremely well to smooth bottoms and edges after the largest drip areas are ground off. I usually don't get much in runs or drips, but once every 4-5 loads. I use the sanding disc always to just freshen up the base, to make certain nothing is there to scratch a table... When I have problems on the side of the pot with a ground area, I follow up with a soft rubber grinder, then a hard buff with tooth paste to polish to the same as rest of pot. Most small areas cannot be found afterwards. This also works with debris that may fall on plates etc.

Good tips! Yes, my old bench grinder finally died and I had to replace it with a new one. I had to take off half the safety stuff to use it, though! I wear goggles and a dust mask always, and often my ear protection if I am grinding several pieces in a row. It is one of the most appreciated tools in the studio and takes glaze drips off very nicely. Diamond bits for the dremel get those smaller spaces.

If the drip is small a Dremel tool with various silicon carbide grinding bits may be better. For larger drips use the bench grinder to get most of the glaze off then use the dremel to finish cleaning the drip so nicely that you can't tell it was ever there. You have to be careful because some of the bits that cut the glaze off best will also cut into the clay so use those carefully and finish with broader bits maybe switching to aluminium oxide bits to finish. It sounds a little complicated but it isn't and the bits are cheap.

Thanks everyone -- I discovered a wonderful tool for this task at the hardware store that attaches to my drill - a 4 inch disc with a backing pad designed for scraping paint and rust off metal - but works beautifully and quickly to sand down glaze, smooth. I finished it with a light sanding of a finer grit sandpaper...and yes, I wore safety glasses and a mask!
I was using my dremel grinding bits in the past for different kind of drips -- but these were pretty serious drips and this solution worked.